Lie-Rinehart algebras, descent, and quantization

Details Lie-Rinehart algebras, descent, and quantization Lie-Rinehart algebras, descent, and quantization

2003-03-02

arxiv.org/abs/math/0303016v1

In: Galois theory, Hopf algebras, and semiabelian categories, Fields Inst. Commun. 43 (2004), 295-316

Mathematics

Symplectic Geometry

AMSTeX 2.1, 23 pages

Scientific paper

A Lie-Rinehart algebra consists of a commutative algebra and a Lie algebra with additional structure which generalizes the mutual structure of interaction between the algebra of functions and the Lie algebra of smooth vector fields on a smooth manifold. Lie-Rinehart algebras provide the correct categorical language to solve the problem whether Kaehler quantization commutes with reduction which, in turn, may be seen as a descent problem.

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